Shape holomorphy of the Calderón projector for the Laplacian in \(\mathbb{R}^2\)

DOI10.1007/s00020-021-02653-5zbMath1472.45011OpenAlexW3180602855MaRDI QIDQ2044585

Fernando Henríquez, Christoph Schwab

Publication date: 10 August 2021

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-021-02653-5

zbMATH Keywords

boundary integral equationsboundary integral operatorsuncertainty quantificationshape holomorphy

Mathematics Subject Classification ID

Analyticity in context of PDEs (35A20) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Integral operators (45P05) Domains of holomorphy (32D05) Boundary element methods for boundary value problems involving PDEs (65N38) Integral representations, integral operators, integral equations methods in two dimensions (31A10)

Related Items (3)

Multi-parameter analysis of the obstacle scattering problem ⋮ Constructive deep ReLU neural network approximation ⋮ Higher-Order Quasi-Monte Carlo Training of Deep Neural Networks

Uses Software

• redbKIT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Shape derivatives of boundary integral operators in electromagnetic scattering. I: Shape differentiability of pseudo-homogeneous boundary integral operators
• Shape derivatives of boundary integral operators in electromagnetic scattering. II: Application to scattering by a homogeneous dielectric obstacle
• Breaking the curse of dimensionality in sparse polynomial approximation of parametric PDEs
• Analyticity of layer potentials and \(L^{2}\) solvability of boundary value problems for divergence form elliptic equations with complex \(L^{\infty }\) coefficients
• A nonlinear integral equation and an iterative algorithm for an inverse source problem
• Boundary integral equations
• Linear integral equations.
• Large deformation shape uncertainty quantification in acoustic scattering
• The inverse scattering problem by an elastic inclusion
• Higher order quasi-Monte Carlo integration for Bayesian PDE inversion
• Nonlinear integral equations for solving inverse boundary value problems for inclusions and cracks
• Material derivatives of boundary integral operators in electromagnetism and application to inverse scattering problems
• Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs
• Shapes and Geometries
• Concrete Functional Calculus
• Higher-Order Quasi-Monte Carlo for Bayesian Shape Inversion
• Second-order shape optimization using wavelet BEM
• Nonlinear integral equations for the inverse electrical impedance problem
• Theoretical Numerical Analysis
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• Frechet differentiability of boundary integral operators in inverse acoustic scattering
• Boundary integral representations of second derivatives in shape optimization
• Shape derivatives for scattering problems
• Electromagnetic wave scattering by random surfaces: Shape holomorphy
• Shape Holomorphy of the Stationary Navier--Stokes Equations
• Higher Order Quasi--Monte Carlo Integration for Holomorphic, Parametric Operator Equations
• Electromagnetic wave scattering by random surfaces: uncertainty quantification via sparse tensor boundary elements
• Inverse elastic scattering from a crack
• On the Frechet differentiability of boundary integral operators in the inverse elastic scattering problem
• Fréchet differentiability of the solution to the acoustic Neumann scattering problem with respect to the domain
• Domain Uncertainty Quantification in Computational Electromagnetics
• Reduced Basis Methods for Partial Differential Equations
• Nonlinear integral equations and the iterative solution for an inverse boundary value problem

This page was built for publication: Shape holomorphy of the Calderón projector for the Laplacian in \(\mathbb{R}^2\)